What is the definition of a knowledge game?

The terms “games” and “play” are not interchangeable.
Consider young boy who is kicking ball about. 
The ball bounces back to him when he kicks it against wall. 
He kicks the ball again after stopping it with his foot. 
The youngster learns to correlate particular motions of his body with the movements of the ball in space by engaging in this type of play. 
This is referred to as associative play.
Consider the child while he waits for companion. 
When the friend arrives, the two boys start walking down the sidewalk together, kicking the ball back and forth. 
The game has now taken on social dimension, with one boy’s actions implying response and vice versa. 
You might believe this type of play can be thought of as an improvised dialogue between two boys using the ball as a medium.

This type of game has no apparent beginning or end, but rather flows from one state to the next.

This might be referred to as “streaming play.”

Imagine the boys arriving at a little park and being bored merely by kicking the ball back and forth.

“Let’s take turns trying to hit that tree,” one boy suggests to the other.

The ball must be kicked from behind this line.”

By dragging his heel into the earth, the youngster makes a line.

“We’ll each kick the ball for a few minutes.”

You gain a point for every time you hit the tree.

The first is to five victories.” They begin to play once the other boy accepts. Now the play has become a game; a fundamentally different kind of play.

Game space: Entering a game involves entering a different kind of space, one in which the rules of everyday life are momentarily suspended and replaced with those of the game space.

A game, in effect, builds a different world, a model world. To enter a game space, players must agree to follow the rules of that area and enter voluntarily.

If people are forced to play, it isn’t a game. This agreement among the players to suspend reality for a short period of time creates a safe environment in which the players can engage in behaviour that would be dangerous, awkward, or even rude in their everyday life.

By agreeing to a set of rules (keep behind the line, take turns kicking the ball, and so on), you can have a lot of fun.

The two lads enter a world that they share. The game would not be possible without such arrangement.